On the density of best coverings in hamming spaces

  • M. Beveraggi
  • G. Cohen
Coding And Combinatorics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 311)


Asymptotical Behavior Private Communication Binary Code Linear Code Good Covering 
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Nous présentons des constructions pour des recouvrements d'espaces de Hamming binaires de dimension n par des sphères de rayon 1. Nous montrons que la densité minimale μn de tels recouvrements est au plus 3/2. Le comportement asymptotique de μn quand n tend vers l'infini n'est pas connu.


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    G.D. COHEN, M.G. KARPOVSKY, H.F. MATTSON, Jr. and J.R. SCHATZ: "Covering radius-survey and recent results", IEEE Trans. Inform. Theory, vol. IT-31, pp. 328–343, 1985.Google Scholar
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    G.L. KATSMAN and S.N. LITSYN: Private Communication.Google Scholar
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    M. MOLLARD: "A generalized parity function and its use in the construction of perfect codes", SIAM J.Alg. Disc. Math., vol 7. no 1, 113–115, 1986.Google Scholar
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    A. LOBSTEIN, G.D. COHEN and N.J.A. SLOANE: "Recouvrements d'espaces de Hamming Binaires", C.R. Acad. Sc. Paris, t. 301, Série I, no 5, pp. 135–138, 1985.Google Scholar

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© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • M. Beveraggi
  • G. Cohen

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